Revisiting the angular momentum dilemma

Abstract

This paper proves that quantization of the square of angular momentum does not vary whether Weyl, simplest symmetric, or Born-Jordan ordering is being used. This shows that no quantization rule is superior over the other, at least in dealing with the
"angular momentum dilemma." The problem, which asks "why is the Weyl quantization of the squared classical angular momentum not equal to the squared angular momentum operator?" is not caused by the choice of ordering rule but rather arises from the von Neumann condition, an equality that was excluded from the axioms of quantization.